Question

a block of wood of mass 4.5 kg is floating in a pond, and oscillating with a frequency of 2.5 hz. what is the effective spring constant of the water?

Answer 1

The effective spring constant of the water is 28.27 N/m.

Step-by-step explanation:

In this case, the block of wood is floating in water and oscillating, behaving like a simple harmonic oscillator. The frequency of oscillation, f, is given as 2.5 Hz. We can relate the frequency of oscillation to the effective spring constant, k, using the formula:

f = 1 / (2 * π) * sqrt(k / m)

Where m is the mass of the block and k is the effective spring constant of the water. Rearranging the equation, we can solve for k:

k = (4 * π^2 * m * f^2)

Substituting the values, with mass m = 4.5 kg and frequency f = 2.5 Hz, we can calculate the value of k:

k = (4 * π^2 * 4.5 * 2.5^2) N/m

Simplifying the expression, the effective spring constant of the water is 28.27 N/m.

Answer 2

To calculate the effective spring constant of water when a block of wood is floating and oscillating in a pond, you can use the formula F = kA, where F is the weight of the block and A is the amplitude of the oscillation.

Step-by-step explanation:

When a block of wood is floating in a pond, it experiences an upthrust force from the water that is equal to its weight. This upthrust force acts as a restoring force when the block oscillates. Therefore, the effective spring constant of the water can be calculated using the formula:

F = kx

Where:

• F is the force on the block (weight of the block)
• k is the effective spring constant
• x is the displacement of the block

Since the block is floating and oscillating vertically, the displacement is equal to the amplitude, which can be calculated using the formula:

x = A

Using the given information, we can calculate the effective spring constant as follows:

F = kA

k = F/A

Where the weight of the block (F) is equal to its mass (m) times the acceleration due to gravity (g). Substituting the values:

F = 4.5 kg × 9.8 m/s²

A = Amplitude (assumed to be given, but not specified in the question)

Once you have the values for F and A, you can substitute them into the formula to calculate the effective spring constant (k).